Quantification of Isotope Fractionation in Experiments with Deuterium-Labeled Substrate

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Quantification of Isotope Fractionation in Experiments with Deuterium-Labeled Substrate

Isotope analysis is a potentially sensitive method to trace in situ degradation of organic contaminants. In a recent paper, Morasch et al. (3) investigated the mechanism of isotope fractionation during toluene biodegradation using deuterium- labeled toluene. The authors overlooked that the Rayleigh equation that is normally used to evaluate isotope fractionation at natural abundance level (2) is not applicable to studies with labeled substrate, particularly if large isotope fractionation occurs. For several of their experiments they obtained negative hydrogen isotope fractionation factors (see Table 1 in reference 3), which contradict the definition of the fractionation factor (see below). Since labeled compound will likely be used in further investigations to study isotope fractionation, it is important to demonstrate why the commonly used Ray- leigh equation is usually not applicable in such studies and to provide an alternative method to quantify isotope fractionation.

The magnitude of isotope fractionation is normally charac- terized by the fractionation factor, which is defined as follows for kinetic isotope fractionation:

␣⫽ H/L

dHp/dLp (1)

whereH and L are the concentrations of the substrate with heavy and light isotopes, respectively, at a given time and dHp

and dLpare increments of product with heavy or light isotopes, respectively, that appear in an infinitely short time (instanta- neous product). In some studies, the fractionation factor is defined by the inverse ratio (2). Since all terms in equation 1 are positive,␣has to be positive. For mass balance reasons,

dHp⫽ ⫺dH

dLp⫽ ⫺dL (2)

Combining equations 1 and 2 and rearrangement leads to dL

L ⫽␣ 䡠 dH

H (3)

Integration of equation 3 fromL

0toLandH

0toHgives ln L

L0⫽␣ 䡠 ln H H0 or H

H0⫽

冉

^L^L⁰

冊

^1/␣ ⁽⁴⁾

Dividing both sides byL/L0 yields R

R0⫽

冉

^L^L⁰

冊

^{共1/␣ ⫺}^1兲 ⁽⁵⁾

whereRandR0are the isotope ratios (H/L) at a given time t and at time zero, respectively. The fraction of substrate that has not reacted yet,f, at timetis given by

f⫽ L⫹H

L0⫹H0⫽ L 䡠共1⫹R兲

L0 䡠共1⫹R0兲 (6) Equations 5 and 6 are analogous to those given by Bigeleisen and Wolfsberg (1), except that here they were derived without any specific assumption about the reaction kinetics and using a different definition of␣andf.

The crucial point is that L/L0 in equation 5 can only be approximated byfif either (i) the concentrations of the heavy isotopes,HandH0, are small, as common for studies at natural abundance level, or (ii) 1⫹R⬇1⫹R0. In the first case, the first expression for f in equation 6 approaches L/L0; in the second case, the second expression can be approximated by L/L0. If one of these two conditions is fulfilled, equation 5 can be simplified to

R

R0⫽f^{共1/␣ ⫺}^1兲 (7)

which corresponds to the Rayleigh equation as used by the authors of the study (3). However, in the experiments with labeled compound presented in the study, condition i is not fulfilled since the compound with deuterium accounts for 50%

of the total toluene concentration. Condition ii is not fulfilled either. For example, for the experiment illustrated in Fig. 1 in reference 3,R0is 1 andRvaries between 1 and about 12 and thus, the assumption that 1⫹R ⬇1⫹R0 holds true is not valid. In other experiments, even higher R values of up to about 54 were observed (see Fig. 2 in reference 3).

By combining equations 5 and 6, an accurate equation is obtained that relatesR,R0,f, and␣:

ln R

R0⫽

冉

^␣¹ ^⫺¹

冊

^䡠 ^ln^共1^⫹^R兲/共1^f ^⫹^R⁰^兲 ⁽⁸⁾

This equation can be used to determine␣by plotting ln(R/

R0) versus ln{f/[(1⫹R)/(1⫹R0)]}. Applying this approach to the data of the experiment with Desulfobacterium cetonicum (as given in Fig. 1 in reference 3), an␣value of approximately 2.7 is obtained instead of⫺5.09. The value of 2.7 is only an approximation, since the data for the calculation were esti- mated from Fig. 1 in reference 3. The calculated value is in the typical range for primary hydrogen isotope effects. Using the correct equation, the introduction of an uncommon parameter to characterize isotope fractionation becomes unnecessary and the data can be discussed in a framework consistent with a large number of studies on isotope fractionation during enzymatic reactions.

Daniel Hunkeler

Center for Hydrogeology University of Neuchatel CH-2000 Neuchatel, Switzerland

Phone: (032) 718 25 60 Fax: (032) 718 26 03

E-mail: [email protected]

, ,

Published in Applied and Environmental Microbiology 68, issue 10, 5205-5207, 2002

which should be used for any reference to this work 1

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3.Morasch, B., H. H. Richnow, B. Schink, and R. U. Meckenstock.2001. Stable hydrogen and carbon isotope fractionation during microbial toluene degradation: mechanistic and environmental aspects. Appl. Environ. Microbiol.67:

4842–4849.

Authors’ Reply

The comments by Dr. Hunkeler provide a valuable extension of our results on basic features of isotope fractionation. In- deed, the fractionation factor ␣n (n for natural abundance) calculated in Morasch et al. (3) is valid to describe isotope fractionation of carbon and hydrogen isotopes only at low abundance of the heavier isotopes (¹³C and D, respectively) as presented in the manuscript. For experiments at elevated abundances of the heavier isotope, the isotope fractionation factor␣l(lfor labeled compounds) should be calculated using equation 3 as given by Bigeleisen and Wolfsberg (1) and men- tioned by Dr. Hunkeler.

In Morasch et al. (3), we used the slopebof a linear regression of the data in a double logarithmic plot of ln(Rt/R0) versus lnf(f⫽ Ct/C0, fraction of substrate remaining [Ct, substrate concentration at timeA;C0, substrate concentration at time zero]) to evaluate the extent of isotope fractionation (equation 2). In experiments with substrates of natural isotope composi- tion,bcan be converted directly to the fractionation factor␣n

or the enrichment factorεwithb⫽1/␣ ⫺1 orε⫽b⫻1,000, because equations 2 and 1 approximate equation 3 at low abundances of the heavier isotope (1, 2).

What is the consequence of using equation 2 instead of equation 3 also in experiments with deuterium-labeled compounds at elevated abundance? In this case, the slopebcalcu- lated by equation 2 becomes a fitting parameter of the data FIG. 1. Simulated hydrogen isotope fractionation experiment for toluene degradation by strain TRM1 as calculated with equation 3 versus equation 1 and␣l⫽ ␣n⫽3.3. The calculations start withR0n⫽ 0.0001 for the simulation of an experiment with natural abundance of deuterium (■) and withR0l⫽1 for the simulation of an experiment with labeled compounds (F).Rtruns fromR0to infinity. At natural abundance of the heavier isotope ln{f/[(1⫹Rt)/(1⫹R0)]} approximates lnfbecauseRtandR0are very small and equation 3 approximates equation 1. Therefore, the slopes of the curves in the range of lnf

⬎ ⫺12 show the deviation in the description of isotope fractionation simulated with equation 1 or 3 for natural abundance (■) and labeled compounds (F). The dashed line depicts the isotope ratio ofRtn⫽1.

TABLE 1. D/H isotope fractionation factors␣orεand fitting parameterbobtained from studies with nonlabeled (␣n) or labeled toluene (␣l)^a

Strain Substrate mixture ␣n ␣l εl b

Desulfobacterium cetonicum Toluene 1.247 1.247 ⫺198.1 ⫺0.198

Toluene-d8and toluene-d3 0.996⫾0.005 4.016⫾5.04 ⫺0.002⫾0.003 Toluene-d3and nonlabeled toluene 3.772⫾1.084 ⫺734.9⫾76.19 ⫺1.251⫾0.034 Toluene-d8and toluene-d5 2.058⫾0.090 ⫺514.1⫾21.25 ⫺0.679⫾0.115 Toluene-d5and nonlabeled toluene 1.009⫾0.017 ⫺8.920⫾16.69 ⫺0.005⫾0.004 Toluene-d8and nonlabeled toluene 3.244⫾0.261 ⫺691.7⫾24.80 ⫺1.196⫾0.075

TRM1 Toluene 3.672 3.650 ⫺726.0 ⫺0.728

Toluene-d8and toluene-d3 0.885⫾0.142 129.9⫾181.3 0.167⫾0.219 Toluene-d3and nonlabeled toluene 3.384⫾0.170 ⫺704.5⫾14.85 ⫺1.280⫾0.080 Toluene-d8and toluene-d5 2.070⫾0.233 ⫺516.9⫾54.38 ⫺0.917⫾0.336 Toluene-d5and nonlabeled toluene 1.014⫾0.012 ⫺13.81⫾11.67 ⫺0.012⫾0.005 Toluene-d8and nonlabeled toluene 3.276⫾0.281 ⫺694.7⫾26.18 ⫺1.219⫾0.254 Thauera aromatica Toluene-d8and nonlabeled toluene 2.543⫾0.567 ⫺606.8⫾87.68 ⫺0.816⫾0.133 Geobacter metallireducens Toluene-d8and nonlabeled toluene 2.550⫾0.187 ⫺607.8⫾28.76 ⫺1.004⫾0.077 Pseudomonas putidastrain mt-2 Toluene-d8and toluene-d3 1.005⫾0.0004 ⫺4.98⫾0.40 ⫺0.016⫾0.003 Toluene-d3and nonlabeled toluene 22.96⫾4.368 ⫺956.4⫾8.29 ⫺4.218⫾0.125 Toluene-d8and toluene-d5 13.65⫾2.452 ⫺926.7⫾13.16 ⫺2.696⫾0163 Toluene-d5and nonlabeled toluene 1.098⫾0.031 ⫺89.25⫾25.71 ⫺0.079⫾0.041 Toluene-d8and nonlabeled toluene 17.78⫾13.46 ⫺943.8⫾42.58 ⫺2.667⫾0.163

a␣nwas calculated with equation 1,␣landεwere calculated with equation 3, andbwas calculated with equation 2.εis calculated asε⫽(1/␣l⫺1)⫻1,000. Average isotope fractionation factors for experiments with mixtures of labeled toluene species␣l, the respective fitting parameterb, and the standard deviations result from three independent growth experiments. Original data were taken from reference 3. Fractionation at natural deuterium abundance was obtained only from a single growth experiment and is not given with a standard deviation.

REFERENCES

1.Bigeleisen, J., and M. Wolfsberg.1958. Theoretical and experimental aspects of isotope effects in chemical kinetics. Adv. Chem. Phys.1:15–76.

2.Mariotti, A., J. C. Germon, P. Hubert, P. Kaiser, T. Letolle, A. Tardieux, and P. Tardieux.1981. Experimental determination of nitrogen kinetic isotope fractionation: some principles; illustration for the denitrification and nitrification processes. Plant Soil62:413–430.

2

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which differs by a constant value from the slopeb⬘calculated via equation 3, where ln(Rt/R0) is plotted versus ln{f/[(1⫹Rt)/

(1⫹R0)]}. The difference in using the two equations is de- picted in Fig. 1 for a hypothetical experiment where the isotope ratioRtruns fromR0to infinity and lnfis plotted versus ln{f/[(1⫹Rt)/(1⫹R0)]}. For natural abundance of deuterium, the slope of lnfversus ln{f/[(1⫹Rt)/(1⫹R0)]} equals 1, indi- cating that the two terms are almost identical as long asRtis smaller than 1. IfRt is larger than 1, the slope of the curve changes and approximates another constant value. Note that the slope of the curve forRt⬎ 1 is similar to the slope of a simulated experiment using labeled compounds withR0⫽1 if the same fractionation factor is applied (Fig. 1). The extent of fractionation is only hypothetical since one could hardly run a real degradation experiment over such enormous concentration ranges. Nevertheless, it shows that the difference in the calculations using equations 1 and 2 or 3 depends on the isotope ratioRtbeing larger or smaller than 1. This property of the calculations becomes especially important if isotope fractionation of elements such as chlorine is studied, where the natural abundances of the heavier and lighter isotopes are almost equal (R0⫽1).

In our experiments the concentrations were usually in the range of 0⬍lnf⬍ ⫺4. Here, the difference of the slopes for labeled compounds and for natural abundance reveals the systematic difference between the two ways of calculation. Figure 1 also shows that the curve for the labeled compounds is not exactly a straight line. However, the experimental error of the isotope analysis is usually much larger than the error by fitting the data with a linear regression, but the description of the data set with equation 3 would certainly improve the interpretation.

With respect to the data produced by Morasch et al., the systematic difference in the description of the data set with equation 2 or 3 results in the same interpretation of the isotope fractionation experiments with deuterium-labeled compounds.

The direct comparison of the obtained isotope fractionations ofband␣clearly shows the relation of isotope fractionation and enzyme mechanisms. The major difference in the use of the two equations is that the absolute value of the commonly used isotope fractionation factor␣can only be calculated from equation 3.

We have recalculated the isotope fractionation factors of the experiments with labeled compounds published in Morasch et al. (3) using equation 3 (Table 1). The recalculated data may provide the reader with fractionation factors comparable to those published in other studies. However, the data show also that an ␣n obtained at a natural abundance of the heavier isotope is not necessarily identical with the ␣l obtained in labeling experiments.

In summary, for experiments with defined conditions the use of deuterium-labeled compounds is an elegant way to over- come the problem of limited availability of isotope mass spec- trometers for D/H analysis and to reduce analysis costs for basic studies of isotope fractionation. Isotope fractionation factor␣should be calculated from labeling experiments with equation 3 but are difficult to relate to isotope fractionation occurring at natural abundance of hydrogen isotopes (3).

ln共Rt/R0兲⫽共1/␣n⫺1兲⫻lnf (1) ln共Rt/R0兲⫽b⫻lnf (2) ln共Rt/R0兲⫽共1/␣l⫺1)⫻ln兵f/关共1⫹Rt兲/共1⫹R0兲兴其 (3)

REFERENCES

1.Bigeleisen, J., and M. Wolfsberg.1959. Theoretical and experimental aspects of isotope effects in chemical kinetics. Adv. Chem. Phys.1:15–76.

2.Mariotti, A., C. Germon, P. Hubert, P. Kaiser, R. Letolle, A. Tardieux, and P.

Tardieux.1981. Experimental determination of nitrogen kinetic isotope fractionation: some principles; illustration for the denitrification and nitrification processes. Plant Soil62:413–430.

3.Morasch, B., H. H. Richnow, B. Schink, and R. U. Meckenstock.2001. Stable carbon and hydrogen isotope fractionation during microbial toluene degradation: mechanistic and environmental aspects. Appl. Environ. Microbiol.

67:4842–4849.

Rainer Meckenstock*

Hans H. Richnow

Center for Applied Geosciences Eberhard-Karls-University of Tu¨bingen Wilhelmstr. 56

72076 Tu¨bingen Germany

*Phone: 49-7071-2973150 Fax: 49-7071-295139

E-mail: [email protected] 3